curve #2855

y² + xy = x³ − 6846036141864580415461343224x + 237743716924884102637037303696937775796288

a-invariants: [1, 0, 0, -6846036141864580415461343224, 237743716924884102637037303696937775796288]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 916399790245882510302
discriminant (Δ): -3882402585839414797511646110356470423294879795340961488571892096822008083913516187648
Faltings height: 14.9690
naive height: 204.0672
primes of bad reduction: 2, 3, 7, 19, 73, 79, 97, 199, 223, 359, 128857
regulator: 485739.624878147792933338167000020544119453272629
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:30 UTC
last updated: 2026-09-26 20:25:30 UTC

(-26582546568208, -633201944397337637368)
(2024596322851172, 91022951659981520271512)
(65776693082151506, 16869713582173882655604260)
(-45826422273095461024/714025, -387630399997951812893481230936/603351125)
(33822779890951982/841, 4041755866523462414580484/24389)

Voznyy (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 31). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:30 UTC · history